Characters of the Symmetric Groups and Correlation Functions of Point Processes
Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 1, pp. 12-28.

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A method for computing the correlation functions of stochastic point processes arising in the decomposition problem for characters of the infinite symmetric group is presented.
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A. M. Borodin. Characters of the Symmetric Groups and Correlation Functions of Point Processes. Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 1, pp. 12-28. http://geodesic.mathdoc.fr/item/FAA_2000_34_1_a1/

[1] Borodin A., Olshanski G., “Point processes and the infinite symmetric group”, Math. Res. Lett., 5 (1998), 799–816 ; http://xxx.lanl.gov/abs/math/ 9810015 | DOI | MR | Zbl

[2] Borodin A., Olshanski G. (to appear)

[3] Vershik A. M., Kerov S. V., “Asimptoticheskaya teoriya kharakterov simmetricheskoi gruppy”, Funkts. analiz i ego pril., 15:4 (1981), 15–27 | MR | Zbl

[4] Daley D. J., Vere-Jones D., An introduction to the theory of point processes, Springer Series in Statistics, Springer-Verlag, New York, 1988 | MR | Zbl

[5] Kerov S., Okounkov A., Olshanski G., , Intern. Math. Res. Notices, 4, 1998 http://xxx.lanl.gov/abs/q-alg/9703037 | DOI | MR | Zbl

[6] Kerov S., Olshanski G., Vershik A., “Harmonic analysis on the infinite symmetric group. A deformation of the regular representation”, C. R. Acad. Sci. Paris, Sér. I, 316 (1993), 773–778 | MR | Zbl

[7] Macdonald I. G., Symmetric functions and Hall polynomials, 2nd edition, Oxford University Press, 1995 | MR | Zbl

[8] Olshanskii G. I., “Unitarnye predstavleniya $(G,K)$-par, svyazannykh s beskonechnoi simmetricheskoi gruppoi $S(\infty)$”, Algebra i analiz, 1:4 (1989), 178–209 | MR

[9] Olshanski G., Point processes and the infinite symmetric group. Part I: The general formalism and the density function, Preprint, 1998 ; http://xxx.lanl.gov/abs/math/9804086 | MR

[10] Borodin A., Point processes and the infinite symmetric group. Part II: Higher correlation functions, Preprint, 1998 ; http://xxx.lanl.gov/abs/math/9804087 | MR

[11] Borodin A., Olshanski G., Point processes and the infinite symmetric group. Part III: Fermion point processes, Preprint, 1998 ; http://xxx.lanl.gov/abs/math/9804088 | MR

[12] Borodin A., Point processes and the infinite symmetric group. Part IV: Matrix Whittaker kernel, Preprint, 1998 ; http://xxx.lanl.gov/abs/math/9810013 | MR

[13] Olshanski G., Point processes and the infinite symmetric group Part V: Analysis of the matrix Whittaker kernel, Preprint, 1998 ; http://xxx.lanl.gov/abs/math/9810014 | MR

[14] Thoma E., “Die unzerlegbaren, positive-definiten Klassenfunktionen der abzählbar unendlichen, symmetrischen Gruppe”, Math. Z., 85 (1964), 40–61 | DOI | MR | Zbl